Simulation of flexible mechanisms in a rotating blade smart-blade applications

SIMULATION OF FLEXIBLE MECHANISMS

IN A ROTATING BLADE FOR SMART-BLADE APPLICATIONS

A. Paternoster, R. Loendersloot, A. de Boer, R. Akkerman

Structural Dynamics and Acoustics,

Faculty of Engineering Technology,

University of Twente,

P.O. BOX 217

7500AE Enschede

The Netherlands

ABSTRACT

The active Gurney flap technology is investigated to improve the performance of rotorblades by allowing helicopter blades to further control the lift unbalance that rises at high speed and by damping vibration loads on the rotor hub. This technology needs validation by wind tunnel testing of a scaled model blade under rotational loading. An optimised geometry of a flexible actuation system has been designed to provide motion for the deployment of the Gurney flap for a Mach-scale model blade [1]. This paper presents the refinement of the flexible actuation system to allow deployment of the Gurney flap and simulation strategies to model the mechanism under loads due to the blade motion and the aerodynamic forces acting on the Gurney flap . The physics domains are addressed separately to be simulated with specific software packages. A co-simulation process permits the simulation of the Gurney flap motion under LMS Virtual.Lab Motion multi-body dynamic software [2] and the simulation of the flexible mechanism under Comsol Multiphysics Finite Element Model software [3]. This simulation scheme successfully models the mechanism under harmonic loads. For faster actuation input, the co-simulation is replaced by a one-way coupling which models the deployment mechanism under loads due to the rotation of the blade, the motion of the Gurney flap and the aerodynamics. The outcome of both simulations shows that the flexible deployment system is suitable for the actuation of the Gurney flap in the two actuation cases presented. The simulation scheme can be applied to simulate similar systems that are under constraints from a large variety of physical domains.

1. INTRODUCTION

Adaptive blades can significantly increase the per-formances of current rotorcraft systems. The effi-ciency and the maximum speed of a rotorcraft in motion depends on the lift provided by the retreat-ing blade which is reduced by the helicopter for-ward speed. The Green Rotorcraft project (part of Clean Sky Joint Technology Initiative) is investigat-ing an active Gurney flap to improve current

rotor-blades [4, 5]. Building a suitable actuation mecha-nism is complex due to the large mechanical and integration constraints present in a rotating rotor-blade. This process involves the development of a one-eighth Mach-scaled model blade to investigate the performance of an active Gurney flap system in a wind tunnel environment.

To meet these challenges the research on flexible designs integrated within a rotorblade led to the

development of a piezoelectric mechanism. This mechanism converts electrical signals into a com-plex motion that permits the deployment and folding of a Gurney flap at the trailing edge of the rotorblade profile [1]. To verify the proper operation of this sys-tem, more complex simulations need to be realised. This paper first summarises the Gurney flap tech-nology and the current status of the research done at Twente University in the scope of Clean Sky JTI [4]. Then, simulation strategies for a multi-physics environment are presented along with results in the case of harmonic actuation and fast deployment.

2. BACKGROUND

2.1. The active Gurney flap concept

The Gurney flap is a small flap placed at the trail-ing edge, of which the length is typically 2% of the profile chord length [6, 7]. It improves the lift of a profile over a wide range of angles of attacks [8]. Furthermore, the Gurney flap provides both a bet-ter static and dynamic stall behaviour [9]. When a helicopter is in forward motion, the pitch angle of the rotorblade between the retreating and the ad-vancing side is adjusted in order to balance the lift difference that rises from the airspeed mismatch as shown in Figure 1. Reverse flow region Helicopter motion Airspeed relative to the blade

Figure 1: Unbalance of the airspeed around a heli-copter in forward motion.

The lift difference limits the helicopter maximum speed because the pitch of the blade can only

com-pensate the lift difference until the profile stall angle of attack is reached. The active Gurney flap aims at enhancing the lift on the retreating side of the heli-copter to allow larger angle of attacks and therefore a faster and more efficient helicopter. As a con-sequence, the Gurney flap needs to be deployed quickly when the blade enters the retreating side. Appropriate performance is achieved when the Gur-ney flap is deployed within 10 degrees of sweeping angle.

Vibratory loads caused by the blade dynamics also limit the efficiency of the rotor, generate discomfort for passengers and noise which should be reduced while flying over densely populated areas. The Gur-ney flap can also actively damp adverse vibrations on the rotor by harmonic actuation at 1/rev, 2/rev and 4/rev [7, 10].

2.2. Mach-scale model blade for wind tunnel testing

The validation of the Gurney flap active system per-formance is an important milestone in the Clean Sky JTI program. Besides the fixed-wing wind tun-nel test, a rotating blade test within a wind tuntun-nel environment is scheduled to verify the correct be-haviour of the Gurney flap for various flight scenar-ios. This requires the development of an actuation system for a Mach-scaled model blade. This sys-tem must answer the specific constraints linked to the scaling of the model blade as shown in Table 1. Table 1: Comparison of the dimensions and the re-quirements for the full scale blade and the Mach-scaled model blade.

Property Full scale Model blade Profile reference Naca 0012 Naca 0012

Blade length 8.15 m 1 m

Rotation speed 26.26 rad/s 210 rad/s

Tip speed 214 m/s 214 m/s

Deployment within 7 ms 1 ms Max g-acceleration 573 g 4500 g 2.3. Flexible deployment actuation mechanism To meet the mechanical constraints, a mechanical system that comprises of piezoelectric patch actu-ators and bending beams has been designed and optimised [1]. The result is a Z-shape system that

amplifies the strains generated by piezoelectric ele-ments into significant horizontal motion close to the trailing edge. Refinement of this design leads to a reverse deployment system that comprises of two actuators to provide a rotational motion of 90 de-gree as shown in Figure 2.

Piezoelectric actuator

Gurney flap

t = 0 ms t = 0.2 ms t = 0.4 ms

Figure 2: Sketch of the refined Z-shape deployment system and detail of the folding motion of the Gur-ney flap.

3. SIMULATION OF A GURNEY FLAP MECHANISM

3.1. Defining and simplifying a multi-physics model

Many physical domains need to be simulated to faithfully simulate a deployment cycle of the Gurney flap mechanism. Modelling a piezoelectric compo-nent requires an electrical domain and a mechani-cal domain. The structure on which the piezoelec-tric component is bonded to is part of the mechani-cal domain as well as the rotorblade in rotation. Fi-nally, there is the aerodynamic domain, which mod-els the interaction of the flow on the Gurney flap and on the rotorblade. The complexity of this problem is summarized in Figure 3.

Although many components are in the mechanical domain, it needs to be broken down to efficiently solve the piezoelectric coupling, the flexible ele-ments of the deployment mechanism and the dy-namics of a rotorblade. From the problem shown in Figure 3 simplifications were made to reduce the coupling between components. The following as-sumptions are made:

• the airflow forces are not applied on the rotor-blade,

• the airflow forces are quasi-static on the Gur-ney flap,

• the voltage is imposed on the piezoelectric component,

• the piezoelectric mechanism has a limited in-fluence on the rotorblade behaviour,

• the blade behaves as a rigid body.

Electrical Mechanical Fluid Piezoelectric mechanism Gurney flap Airflow Rotorblade

Figure 3: Distribution of physics domains across the components to simulate.

These assumptions lead to a reduction of the com-plexity of the problem as shown in Figure 4. The physical domains are distributed across 3 simula-tion environments. The multi-body simulasimula-tion that comprises the rotorblade in rotation with the Gurney flap is performed with LMS Virtual.Lab Motion soft-ware [2]. The piezoelectric mechanism is modelled through Comsol Multiphysics within the piezoelec-tric physics environment [3]. The CFD simulations are performed with Comsol Multiphysics within the turbulent flow environment. These softwares were chosen for their capabilities to interface with lab: Comsol 4.2 can be executed as part of a Mat-lab script and Virtual.Lab Motion models can be ex-ported as Simulink models where Virtual.Lab Mo-tion solver can process them.

Multi-Body

FEM - CFD FEM - Coupled

Piezoelectric mechanism

Airflow Gurney flap

Rotorblade

2

3 1

Figure 4: Model investigated. The connections be-tween the softwares are 1 one-way coupling, 2

co-simulation and 3 data lookup table.

As shown in Figure 4, the connections between the simulations are kept to a minimum. The blade being hardly influenced by the motion of the mechanism a one-way coupling is set-up. The acceleration of the blade at the position of the mechanism is used to provide inertia forces in the mechanism during rota-tion (Figure 4 1 ). A co-simulation process provides exchange of force and displacement data between the Gurney flap and the piezoelectric mechanism (Figure 4 2 ). The force the airflow applies on the Gurney flap is taken into account with a data table comprising pressure data from a large set of CFD simulations under various conditions (Figure 4 3 ). 3.2. Models considered

3.2.1. Piezoelectric FEM simulation

The mechanism is modelled in Comsol Multiphysics as a two-dimensional structure using plain strain as-sumption. A contact model is added to take the con-tact between the structure and the skin of the rotor-blade profile into account. Finally the motion of the end part that drives the deployment of the Gurney flap is constrained to follow the kinematic relations set up in the multi-body dynamics model.

3.2.2. Rotorblade and Gurney flap multi-body simulation

The rotorblade is modelled as a rigid body. The hub of the rotorblade is modelled based on the blade definition for the full scale version of the blade. The rotorblade is trimmed to maintain zero pitch.

3.3. Coupling FEM analysis to Multi-body-Dynamics

Performing simulations of rotating elements within a multi-body dynamics software while keeping the simulation of flexible elements for a Finite Element Method, allows to maximise the efficiency of both solvers. Coupling these two solvers means ex-changing force and displacement data. This is per-formed through a modified ping pong scheme. In a ping pong scheme the simulation is cut into time-steps at which data is passed from one solver to another [11, 12] as shown in Figure 5. The flexi-ble piezoelectric mechanism simulation outputs dis-placements to the Gurney flap in the multi-body simulation that are applied as translations. The multi-body dynamics software calculates the reac-tion forces that are a sum of the forces due to the inertia, the imposed translations and aerodynamic pressure. This data is sent back to the FEM model of the piezoelectric mechanism with the accelera-tion of the blade due to its moaccelera-tion.

FEM FEM Multi-body Multi-body

t

t

t

t

Figure 5: Ping pong scheme for co-simulation. The last computed values of the force and the displace-ment are exchanged at the time-step.

Investigation of the scheme is done through mass-spring systems. Early analyses show that a very small time-step is required to keep both solvers sta-ble. In order to increase the time-step, the scheme is modified to provide more data to the multi-body simulation. This time the FEM analysis commu-nicates data corresponding to the entire time-step. The multi-body simulation is run for the same time-step taking the complete time data of the displace-ment into account. The force obtained from the

multi-body simulation for that time-step is extrapo-lated for the following time-step before sending it to the FEM analysis as shown in Figure 6. This mod-ified scheme provides better stability for the same time-step size. FEM FEM Multi-body Multi-body

t

t

t

t

Figure 6: Modified ping pong scheme for co-simulation. The FEM sends the displacement of the full time-step while the multi-body simulation sends the force extrapolated for the next time-step. The extrapolation function has a great influence on the outcome of the simulation, especially when the driving voltage is not smooth. The displacements calculated by the co-simulation scheme can vary significantly depending on the extrapolation func-tion chosen as shown in Figure 7.

0 0.1 0.2 0.3 0.4 0.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (s) Displacement (mm) Linear 2nd _{order function} Last value

Figure 7: Displacement calculated on a simplified system using 3 different extrapolation functions to predict the force applied in the FEM when a square profile is used as voltage input.

A linear extrapolation tends to overestimate the

loads which excites the structure further more. Choosing the value at the end of the time-step re-moves dynamic effects from the system. In this ex-ample, the second order polynomial provides the best results and is chosen for this model. The co-simulation process is therefore limited to situations where the loads are smooth and where the system has a response close to the extrapolation function. 3.4. CFD - lookup table

A quasi-static 2D turbulent CFD model is set up to estimate the force acting on the Gurney flap over the large combination of conditions for the rotor-blade and the Gurney flap. The variables taken into account are:

• the velocity of the airflow far from the blade,

• the angle of attack of the profile,

• the deployment angle of the Gurney flap.

The force increases with larger angles of attack, de-ployment angles and airflow speeds as shown in Figure 8. This force is implemented in the multi-body simulation as an external force and is calcu-lated as a function of the three parameters men-tioned earlier by an external function for each time-step of the Virtual.Lab Motion solver.

0 20 40 60 80 −10 0 10 5 10 15 20 25 Ma 0.6 Ma 0.5 Ma 0.4 Ma 0.3 Ma 0.2

Angle of attack (deg) Deployment angle (deg)

Normal force (N/m)

Figure 8: Force acting on the Gurney flap for vari-ous airflow speeds as a function of the angle of at-tack of the profile and the deployment angle of the Gurney flap.

4. RESULTS AND DISCUSSION

4.1. Forced deployment with no blade rotation The co-simulation process was sufficient to cor-rectly simulate harmonic deployment of the Gurney flap at low frequencies (210 rad/s – 1/rev) for a fixed blade. Separating the force applied by the flow re-veals that the airflow is the main force acting on the piezoelectric mechanism as shown in Figure 9.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 −0.5 0 0.5 1 1.5 2 2.5 Inertia forces (N) Aerodynamic forces (N) Time (s)

Force on the mechanism (N)

Figure 9: Force acting on the mechanism when de-ploying the flap at 210 rad/s (1/rev).

Unfortunately, the co-simulation process was un-able to provide insight for deployment speeds in the range of the requirements for the fast Gurney flap deployment. This is due to the instability of the co-simulation during faster operation. Decreasing the time-step may solve that issue but requires extra computation time and power that was unavailable. Further improvements can be formulated to refine the co-simulation scheme.

A simplified analytical expression of the system can be chosen as an extrapolation function to better re-flect the dynamics of the system and therefore in-crease the stability of the simulations. For systems with a short response time, it might be of interest to modify the co-simulation process by solving the same time-step multiple times until the error be-tween the two solvers for one parameter is below a defined threshold.

4.2. Blade simulation under rotation.

To simulate faster and step actuation profiles, the co-simulation is replaced by a one way coupling as shown in Figure 10. Multi-Body FEM - CFD FEM - Coupled Piezoelectric mechanism

Airflow Gurney flap

Rotorblade

2

3 1

Figure 10: Model investigated. The connections be-tween the softwares are 1 one-way coupling, 2

co-simulation replaced by one-way coupling and 3

data lookup table.

The multi-body simulation and the FEM are there-fore independent. First the multi-body simulation is performed with the airflow force acting on the Gur-ney flap. The blade is accelerated until the opera-tional rotation speed of 2000 rpm is reached. Then, the Gurney flap is actuated by a position driver with follows the following profile: the flap is first folded within 1 ms before being deployed after half a blade revolution within the required 1 ms. Data concern-ing the reaction forces and the acceleration of the blade due to its rotation is stored.

This data is then used in the FEM analysis to take into account the effect of the vertical and longitu-dinal acceleration due to the rotation of the blade and the lead/lag motion. A voltage profile is ap-plied to the piezoelectric components following the same square profile applied in the multi-body sim-ulation. In the multi-body simulation, contrary to the harmonic deployment case, the forces on the mechanism due to the dynamics of the blade and the forces due to the airflow have the same order of magnitude as shown in Figure 11 (a). Combina-tion of the two force gives the force the mechanism need to deliver for a 1 ms deployment as shown in Figure 11 (b).

Actuation Inertia forces (N) Aerodynamic forces (N) 4.8 4.85 4.9 4.95 5 5.05 5.1 −1.5 −1 −0.5 0 0.5 1 1.5 Time (s)

Force on the mechanism (N)

(a) Folded Deployed Deployed 5.01 5.015 5.02 5.025 5.03 −1.5 −1 −0.5 0 0.5 1 1.5 Time (s)

Force on the mechanism (N)

(b)

Figure 11: (a) Oscillations of aerodynamic and iner-tia forces on the mechanism over multiple rotations of the helicopter blade. (b) Force on the mecha-nism during the folding and deployment phase of the Gurney flap.

This data is then included in the FEM analysis of the piezoelectric mechanism along with the loads due to the blade rotation. The resulting transient analysis shows that the piezoelectric mechanism is capable of switching the deployed and folded po-sition within the required deployment duration as shown in Figure 12. However as damping is not implemented inside the FEM analysis significant vi-brations are present in the folded position and once the flap is deployed again. In the final mechanism, control will be applied on the piezoelectric actuator to ensure correct positioning and avoid the excita-tion of the deployment system.

5.01 5.015 5.02 5.025 5.03 5.035 40 15 -10 -35 -55 65 90 Time (s)

Deployment angle (deg)

Folded Deployed Deployed

Figure 12: Deployment angles computed by the FEM analysis.

5. CONCLUSION AND FUTURE WORK

Adaptive blade technologies can significantly in-crease helicopter performances by tuning a blade characteristics to the surrounding aerodynamic conditions. The Gurney flap concept provides a mean to change these characteristics and the Z-shape actuation system provides the required force and displacement to deploy it according to quasi-static simulations. This paper explores simulation processes to model a set of physical domains to get realistic insights on the Gurney flap performances under two main types of loading. The harmonic deployment for vibration and noise control can be simulated with the proposed co-simulation scheme. In the case of a fast deployment in the retreating side of the helicopter, the co-simulation is not sta-ble enough to simulate the motion of the Gurney flap. The alternative method presented decouples the multi-body simulation that provides the reaction loads from the FEM analysis which calculates the displacements. Therefore, the simulations are run separately and provide a detailed analysis of the loads the flap is subjected to and demonstrates that the Z-shape mechanism can switch from one con-figuration to another within the required 1 ms. This paper proves the relevance of flexible piezo-electric mechanism for the deployment of the Gur-ney flap which comply with the mechanical con-straints of a Mach-scale helicopter model blade. Fu-ture work include the manufacturing of a prototype and its testing fixed in a wind-tunnel.

The simulation processes presented in this paper can be applied to similar situations where many tools are required to model complex physical do-mains.

6. ACKNOWLEDGEMENTS

LMS is gratefully acknowledged for its participation in this study and especially Yves Lemmens for his contribution and expertise on modelling using LMS Virtual.Lab Motion.

This project is funded by the Clean Sky Joint Tech-nology Initiative (grant number [CSJU-GAM-GRC-2008-001]9) - GRC1 Innovative Rotor Blades, which is part of the European Union’s 7th Framework Pro-gram (FP7/2007-2013).

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